Though not as ubiquitously recognizable as hierarchical assembly is, generative fixation underlies progress in many areas. Like in the video industry for instance, which only really took off once the VHS/Betamax war had run its course. The “fixation” of VHS within this industry in essence generated new opportunities for advancement. For example, it permitted the development of the video rental business, which brought films from the back rooms of studio houses into living rooms everywhere. Had the tussle between VHS and Betamax continued, many of these opportunities might not have presented themselves. The economics of supporting two formats simultaneously would have been economically crippling for the fledgling industry.

VHS v. Betamax was a case where two contestants competed for dominance along a single dimension—the format accepted by video players. Consider a scenario consisting of multiple dimensions and multiple contestants in each dimension. Suppose, moreover, that no contestant in any dimension is outright superior. That is, the superioriority/non-superiority of the contestants in each dimension is dependent on the state of the contests in the other dimensions. This scenario describes the most commonly arising situation in natural evolution. Here, the “dimensions” are genetic loci, and the “contestants” are alleles. (Statistically, the scenario just described is more likely than one where one or more locus has an allele that is superior regardless of the frequencies of the alleles at other loci.)

The danger in such cases is that progress will stall because no contestant will come to dominate its dimension. The generative fixation hypothesis holds that in a system undergoing recombinative evolutionary dynamics, progress will continue. Although no locus has an allele that is outright superior, a small number of  alleles belonging to different dimensions that play nice together (i.e. confer above average fitness as a group) will come to dominate their respective dimensions. In doing so, they will set the stage for the next multi-dimensional contest over the remaining dimensions. And so on.

I’ve demonstrated the genetic algorithm’s ability to scaleably identify and fix synergistic sets of unlinked non-competing alleles in a recent manuscript and in my dissertation.

Click here to see the final version (single spaced for easy reading).

The foundations of most computer engineering disciplines are almost entirely mathematical. There is, for instance, almost no question about the  soundness of the foundations of such engineering disciplines as graphics, machine learning, programming languages, and databases. An exception to this general rule is the field of genetic algorithmics, whose foundation includes a significant scientific component.

The existence of a science at the heart of this computer engineering discipline is  regarded with nervousness. Science traffics in provisional truth; it requires one to adopt a form of skepticism that is more nuanced, and hence more difficult to master than the radical sort of skepticism that suffices in mathematics and theoretical computer science. Many, therefore, would be happy to see science excised from the foundations of genetic algorithmics. Indeed, over the past decade and a half, much effort seems to have been devoted to turning genetic algorithmics into just another field of computer engineering, one with an entirely mathematical foundation.

Broadening one’s perspective beyond computer engineering, however, one cannot help wondering if much of this effort is not a little misplaced. Clearly, as fields of engineering go, genetic algorithmics is not the exception—the foundations of most engineering fields include large scientific components. What seems to matter is, not the  existence of a science within the foundation of an engineering discipline, but the state of that science. The advanced state of physics and chemistry is, for example, a significant part of the reason for the advanced state of such fields as mechanical, chemical, civil, aeronautical and electrical engineering.

Historically, the blossoming of a field of engineering has typically had to await the maturation of certain underlying field(s) of science. Consider for a moment the improbability of  constructing an internal combustion engine based on the phlogiston theory of combustion. Even if one somehow succeeds in actually building a prototype, further advances within the rubric of phlogiston theory would probably be limited. Combustion engine engineering would be a black art.

I trust that the scenario just described will give users of genetic algorithms and would-be inventors of new genetic algorithms pause, and reason for hope. Pause because even after decades of research, “black art” about sums up the process of applying current genetic algorithms and inventing viable new ones. Hope because it is conceivable that just as Lavoisier’s oxygen based theory of combustion stimulated rapid advances in the construction of internal combustion engines, fundamental upheavals in the science of genetic algorithmics might stimulate rapid advances in the ways in which genetic algorithms are applied and improved.

Given the above, the following question seems to get at  the heart of the matter: What should a science of genetic algorithmics, one capable of stimulating advances in the construction and application of genetic algorithms, look like? I submit that such a science should be organized around the search for a minimal set of computational efficiencies possessed by the simple genetic algorithm such that when considered together these efficiencies explain the adaptive capacity of the simple genetic algorithm on a very broad range of fitness functions. Roughly, computational efficiencies should play the part played by scientific laws in the physical sciences. The challenge is to identify the minimal set with the widest possible explanatory power.

There are two important reasons for making the simple genetic algorithm the object of attention. The first is precedence. There already exists a well known body of science with this algorithm as its focus. This pre-existing work, specifically the theory that goes by the name of the building block hypothesis, provides a point of reference against which future theories may be compared. The second reason is biological plausibility. Unlike many genetic algorithms currently in use, the simple genetic algorithm contains no biologically implausible mechanisms and is, therefore, a legitimate model of sexually evolving biological populations. Such populations have been the subject of intense scientific scrutiny for well over a century and have generated an enormous amount of scientific work. This body of work can serve as a second point of reference.

The aforementioned outline for a science of genetic algorithmics is hardly novel. Until about the mid 1990s, the study of genetic algorithms was organized roughly along the lines just described, with implicitly parallel building block discovery, and implicitly parallel hierarchical assembly being the core computational efficiencies that the simple genetic algorithm supposedly parlayed into a powerful capacity for general purpose adaptation. Problems arose when researchers were unsuccessful in their attempts to rigorously derive complexity theoretic bounds that showcased these purported core efficiencies. Much more seriously, efforts to demonstrate these efficiencies experimentally also proved unsuccessful. The consequence for the building block hypothesis in theoretical circles was severe—rightfully so.

Unfortunately, so was the consequence for the overarching scientific program described above. If there is just one thing readers take away from this dissertation, I hope it’s the sense that this program is viable.

Dissertation webpage

Download manuscript